Problem: $ D = \left[\begin{array}{rrr}1 & 2 & -2\end{array}\right]$ $ F = \left[\begin{array}{rrr}3 & -2 & 1\end{array}\right]$ Is $ D+ F$ defined?
Explanation: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ D$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ D$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ D$ ) must equal $ q$ (number of columns in $ F$ Do $ D$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ D$ and $ F$ have the same number of columns? Yes Yes No Yes Since $ D$ has the same dimensions $(1\times3)$ as $ F$ $(1\times3)$, $ D+ F$ is defined.